It has been well known for many years that the rate at which the gas in a mixture of gases condenses is reduced by the presence of non-condensing gases in the mixture. The problem has been recognised by manufacturers of condensers for steam turbines used in electricity generation, and by manufacturers of many other types of plant. Condensation heat transfer is however difficult to measure as it is a rapid and violent process in which a large quantity of heat is transferred through an interface across which the temperature difference is intentionally small.
The physics of condensation of a pure gas is well known. This condensation process can best be understood by considering the simple situation of a flow of pure gas normal to a vertical surface that is maintained at a constant temperature by a cooling system such that the gas condenses on the vertical surface. Once equilibrium has been established, at every location on the surface a film of condensate forms at a rate that is constant. The condensate runs down the surface under gravity but once equilibrium has been established at any given location the film of condensate is of a constant thickness. Substantially, the variation in temperature in the bulk gas normal to the surface is negligible, and so the temperature difference between the bulk gas and the vertical surface is entirely across the thickness of the condensate film. These physical processes are sufficiently well understood to enable the design of simple heat exchangers for condensing pure gases without referring to empirical correlations.
It will be appreciated that generally the gas flow towards a cooled surface in a condensation plant is not all normal to a plane vertical surface. A common arrangement is a “shell and tube” structure which has a “nest” of parallel horizontal tubes through each of which tubes a cooling liquid is passed. Gas condenses on the cold outer surfaces of the tubes and droplets of condensate fall from the tubes. Some of these droplets land on lower tubes, thereby increasing the thickness of the film of condensate on those tubes and increasing the resistance to heat transfer. This process, called inundation, complicates the estimation of the performance of such condensers and accordingly empirical correlations are generally used to predict the overall performance of such systems.
Whereas the physics of condensation of pure gases is relatively simple, the physics of condensation of a mixture of gases is considerably more complicated. The energy released per unit of gas condensed is of course the same for mixtures as for pure gases, but the rate at which energy can be transferred between the mixture of gases and the condensing surface is significantly reduced by the presence of the non-condensing gas or gases.
As in the case of a pure gas, when equilibrium is established, gas condenses to form a film of condensate on the heat exchange surface at a rate that is constant. Condensate runs down or falls off the surface at the same rate as it forms, and in the case of a vertical cooling surface a film of condensate is formed which is of constant thickness at any given location. It has been found however that the concentration of the non-condensing gas or gases increases in a boundary layer of gas between the bulk gas and the condensate film. This increase in the concentration of non-condensing gas results from the fact that non-condensing gas is swept towards the cooling surface with the condensing gas and accumulates adjacent the cooling surface. This increases the non-condensing gas mass fraction in the boundary layer, which restricts the flow of the condensing gas towards the condensing surface.
The problems that arise when condensing a first gas from a mixture of gases as a result of the presence of non-condensing gases have been appreciated for many years. It appears however that the practical significance of this problem has been underestimated. To assist understanding of this problem, the impact of the problem on condensing steam from a mixture of steam and air is discussed below.
If a mixture of steam and air, at the saturation temperature of the steam, flows normal to a plane vertical cooled surface maintained at a constant temperature below the boiling point of water, when the steam and air mixture arrives at the cooled surface steam condenses to form a film of water on that surface. Air in the mixture however remains in the form of molecules of its constituent gases. The presence of this air impedes the flow of more steam molecules to the surface of the water film. The rate at which air can diffuse back against the flow of steam limits the rate at which steam can flow towards the cooled surface. Thus a boundary layer forms in which the air mass fraction increases from a substantially uniform generally low value in the bulk gas to a substantially higher value at the surface of the water film. Given that the pressure of the gas mixture everywhere in the condenser is the sum of the local partial pressures of the steam and the air and that the flow distance through the boundary layer from the bulk gas to the condensate film is small, the total pressure at both sides of the boundary layer must be substantially the same. At the surface of the condensed water film, the steam must be at saturation temperature. Given that the air partial pressure at the surface of the water has increased, the steam partial pressure there has reduced. Therefore the saturation temperature of the steam there is also reduced, and a temperature difference has developed across the boundary layer.
Generally an equilibrium situation is quickly established. Thus, although with the condensation of a pure gas the variation in temperature of the bulk gas normal to the cooled surface is negligible, and the bulk gas in effect extends up to the surface of the condensate film, with a steam/air gas mixture there is a temperature difference between the bulk gas and the surface of the water film that has condensed out of the mixture. The total temperature difference between the bulk gas and the cooled surface upon which steam condenses is dropped across the total width of the boundary layer plus the condensate film, but the temperature difference across the boundary layer is substantially more significant than the temperature difference across the condensate film.
The above problem has been discussed in the context of a plane vertical cooling surface, but generally condensers do not have such a simple structure and therefore inundation further complicates the estimation of the performance of the plants. As a result many empirical correlations are generally necessary during the design of condenser plant. Although the problems encountered in condensing one gas of a mixture of gases has been described in the context of steam/air mixtures, it will be appreciated that other gas mixtures behave in a similar way.
The effects of non-condensing gas in condensers are, of course, reduced if a flow of the mixture is imposed parallel to the heat exchange surfaces. This reduces the concentration of the non-condensing gas or gases adjacent to the heat exchange surfaces. Generally the known problems associated with non-condensing gases in condensers have been addressed by imposing flows relative to the heat exchange surfaces. Nevertheless, although the principles of the processes have been understood for some time, it has not been possible readily to predict the rate at which the processes proceed with accuracy and therefore, in practical condensing plant, it has been conventional to rely upon empirical correlations when estimating the surface area required for a condenser heat exchanger. Of course, a difficulty when relying upon empirical correlations is that it is not easy to predict the performance of a “perfect” plant so the extent of any short fall of performance may not be recognised. Furthermore, if any of the correlations relied upon are not quite correct, the overall design cannot be optimum.
Further details of the effects of non-condensing gas on condensation processes are given in “Convective Boiling and Condensation”, chapter 10, J G Coilier, ISBN 0-07-011798-5. This includes a discussion of condensation in the present of a non-condensing gas and reports calculations of the effects of the non-condensing gas on reducing the heat transfer coefficient for both no imposed flow (also known as free convection), and for an imposed flow (also known as forced convection). “Condensation of a Vapour in the Presence of a Non-conducting Gas”, J W Rose, Int J Heat Mass Transfer Vol. 12 pp 233-237 1969 compares the results of a simplified calculation method with the results for free convection.
An experiment measuring the heat transfer of interest is described in “Measurements of Condensation Heat Transfer Using a Variable Conductance Heat Pipe”, J A Robinson et al, Second UK National Heat Transfer Conference, ImechE 1988. This paper describes a technique of measurement of the effect of a mixture of steam and air condensing on a vertical thin disc. Some measurements of heat transfer coefficient at different air mass fractions are plotted. The anticipated effect of an imposed velocity parallel to the condensing surface on some reduction of the dependence of the heat transfer coefficient on air mass fraction is also shown.